A classroom has \(x\) rows, with \(x+3\) students in each row. If there are 180 students in total, how many rows are there?
Answer and explanation
Correct answer: 12
Let the number of rows be \(x\). Then the total number of students is \(x(x+3)=180\), so \(x^2+3x-180=0\). Factoring gives \((x+15)(x-12)=0\), hence \(x=12\) or \(x=-15\). Since the number of rows cannot be negative, the valid answer is 12. Exam tip: For arrangement problems, write total objects = number of rows × objects in each row.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Let the number of rows be \(x\). Then the total number of students is \(x(x+3)=180\), so \(x^2+3x-180=0\). Factoring gives \((x+15)(x-12)=0\), hence \(x=12\) or \(x=-15\). Since the number of rows cannot be negative, the valid answer is 12. Exam tip: For arrangement problems, write total objects = number of rows × objects in each row.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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